They don't like using the term, presumably because it has very different connotations to Christians so may be misunderstood. The Quran pretty clearly calls Jesus the Messiah though, so it'd be hard to dismiss.
'O People of the Scripture, do not commit excess in your religion or say about Allāh except the truth.
The Messiah, Jesus the son of Mary, was but a messenger of Allāh and His word which He directed to Mary and a soul [created at a command] from Him. So believe in Allāh and His messengers. And do not say, "Three"; desist - it is better for you. Indeed, Allāh is but one God. Exalted is He above having a son. To Him belongs whatever is in the heavens and whatever is on the earth. And sufficient is Allāh as Disposer of affairs.'
Messiah In Quran The word Messiah mentioned in Quran: detail in English and Arabic. QURAN TOPICS MAIN PAGE MIRACLES & WONDERS IN QURAN The word المسيح mentioned in Quran. Quranic Verses about Messiah. The word Messiah
www.thelastdialogue.org